I'm studying the SSH model, here's the reference. I don't get what the definition of a topological invariant is in this case. I think the important property is that the winding number cannot be changed without either breaking a symmetry of the system or closing the bulk band gap, but why do we call it a topological invariant?
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2$\begingroup$ Does this help? $\endgroup$– Kartik ChhajedCommented Jul 30, 2020 at 16:34
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$\begingroup$ It does! It still seems more of an analogy though, not really a full explanation, or am I missing something? $\endgroup$– Karim ChahineCommented Jul 30, 2020 at 21:03
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1$\begingroup$ It's called a topological invariant because the winding number of a continuous function is indeed a topological invariant, a concept defined in the branch of mathematics called algebraic topology. $\endgroup$– PPRCommented Aug 19, 2020 at 4:04
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1 Answer
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To some extent, the time-reversal symmetry and the inversion symmetry protect the topological phase. This phenomenon is called symmetry protected topological phases--SPT. So when winding number is equal to 1(0), it is a topological(trivial) phase. The two regimes can not be smoothly connected by continuously deforming the mapping without closing the gap.
